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Scale 3623: "Aerocrian"

Scale 3623: Aerocrian, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Aerocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,9,10,11}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3215
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 319
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area2.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF{5,9,0}142
A♯{10,2,5}331.33
Minor Triadsdm{2,5,9}221.33
a♯m{10,1,5}221.33
Augmented TriadsC♯+{1,5,9}331.33
Diminished Triads{11,2,5}142
Parsimonious Voice Leading Between Common Triads of Scale 3623. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F a#m a#m C#+->a#m A# A# dm->A# a#m->A# A#->b°

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius2
Self-Centeredno
Central Verticesdm, a♯m
Peripheral VerticesF, b°

Modes

Modes are the rotational transformation of this scale. Scale 3623 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3859
Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
3rd mode:
Scale 3977
Scale 3977: Kythian, Ian Ring Music TheoryKythian
4th mode:
Scale 1009
Scale 1009: Katyptian, Ian Ring Music TheoryKatyptian
5th mode:
Scale 319
Scale 319: Epodian, Ian Ring Music TheoryEpodianThis is the prime mode
6th mode:
Scale 2207
Scale 2207: Mygian, Ian Ring Music TheoryMygian
7th mode:
Scale 3151
Scale 3151: Pacrian, Ian Ring Music TheoryPacrian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [3623, 3859, 3977, 1009, 319, 2207, 3151] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3623 is 3215

Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3623 is chiral, and its enantiomorph is scale 3215

Scale 3215Scale 3215: Katydian, Ian Ring Music TheoryKatydian

Transformations:

T0 3623  T0I 3215
T1 3151  T1I 2335
T2 2207  T2I 575
T3 319  T3I 1150
T4 638  T4I 2300
T5 1276  T5I 505
T6 2552  T6I 1010
T7 1009  T7I 2020
T8 2018  T8I 4040
T9 4036  T9I 3985
T10 3977  T10I 3875
T11 3859  T11I 3655

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 3591Scale 3591, Ian Ring Music Theory
Scale 3607Scale 3607, Ian Ring Music Theory
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3687Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3111Scale 3111, Ian Ring Music Theory
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 1575Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.